Local projection stabilization methods for \boldsymbolH(\rm curl) and \boldsymbolH(\rm div) advection problems

2025/05/22 by Yangfan Luo, Jindong Wang, Luo, Yangfan +3 · 1 citation
Engineering · #65N12 #65N60 #Advanced Numerical Methods in Computational Mathematics #Computational Fluid Dynamics and Aerodynamics #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods in engineering

paper · pdf · doi:10.48550/arxiv.2505.16468

openalex publication_date 2025/05/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We devise local projection stabilization (LPS) methods for advection problems in the \boldsymbolH(curl) and \boldsymbolH(div) spaces, employing conforming finite element spaces of arbitrary order within a unified framework. The key ingredient is a local inf-sup condition, enabled by enriching the approximation space with appropriate \boldsymbolH(d) bubble functions (with d = curl or div). This enrichment allows for the construction of modified interpolation operators, which are crucial for establishing optimal a priori error estimates in the energy norm. Numerical examples are presented to verify both the theoretical results and the stabilization properties of the proposed method.

Citations

• Exponentially-fitted finite elements for H(\rm curl) and H(\rm div) convection-diffusion problems
• A hybridizable discontinuous Galerkin method for magnetic advection-diffusion problems
• Discontinuous Galerkin methods for magnetic advection-diffusion problems
• Simplex-averaged finite element methods for H(\rm grad), H(\rm curl) and H(\rm div) convection-diffusion problems
• Eulerian and Semi-Lagrangian Methods for Convection-Diffusion for\n Differential Forms

Cited by

• A streamline upwind/Petrov-Galerkin method for the magnetic advection-diffusion problem

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